Question

an algebraic expression that gives the area of a circle with a radius r

Answer 1

You are looking for the area formula of a circle. Which is \[A=\pi r^{2}\]

Answer 2

Let's make c = circumference. The circumference of a circle is: \[C=\ 2\Pi r\] and the area formula is: \[A= \pi r ^2\]First, let's solve for r in the circumference equation. Divide each side by \[2\pi\]You will have only 'r' on the right side of the equation. So now you have the radius. \[ \frac{ C }{ 2\pi } = \frac{ r*2\pi }{ 2\pi }\]
Now, plug in 'r' to the second equation (Area formula).
\[A= \pi r^2\] you will have something that looks like this: \[A=\pi (\frac{ C }{ 2\pi })^2\] Then, square what's inside the bracket to get:
\[A=\pi*\frac{ C^2 }{ 4\pi^2 }\]Since you have pi on top and bottom, cancel them out. Your final answer will be :\[\frac{ C^2 }{ 4\pi }\]That is your expression. Don't add in 'A=" because the '=' make it an equation. Good luck!